A  NEW  SYSTEM  OF  HARMONY 


Based  on 


Four  Fundamental  Chords 
EDUARDO  GARIEL 


NEW  YORK    G.  SCHIRMER 


Southern  Branch 
oftKe 

University  of  California 

s  Los  Angeles 


rj 


This  book  is  DUE  on  the  last  date  stamped  below. 
MAY   8     1925 


OCT  2  9  192ff 

- 

JAN  2  8  1935 
y  23  1935 


MAN 


MAR  1 2  1947 

6  1 


5m-8,'21 


NOV  2  9  1949 


B 


'59 

APfl  1  5  '59 
MAY  6    'I? 


A 

NEW  SYSTEM  OF  HARMONY 

BASED   ON 

FOUR  FUNDAMENTAL  CHORDS 


BY 

EDUARDO   GARIEL 

TEACHER  OF  MUSICAL  COMPOSITION  AT  THE  NATIONAL  CONSERVATORY  OF  Music 

IN  THE  CITY  OF  MEXICO  ;  CHIEF  SUPERVISOR  OF  SCHOOL  Music,  AND 

TEACHER  OF  THE  METHODOLOGY  OP  SCHOOL  Music  AT 

THE  BOYS'  NORMAL  SCHOOL,  IN  THE  SAME  CITY 


SECOND  EDITION 


G.   SCHIRMER 

BOSTON      .-.      NEW  YORK     .'.      LONDON 


Depositado  conforme  a  la  ley  de  la  Republics  Mexicana  en  el  afio 
MCMXVI  por  G.  SCHIRMBR  (Inc.),  Propieurios,  Nueva  York  y  Mexico 

Copyright,  1915,  by  EDUARDO  GARIEL 
Copyright,  1916,  by  G.  SCHIRMER 


MUSIC 
LIBRARY 

MT  50 


To 
VENUSTIANO  CARRANZA 

First  Chief  of  the  Constitutionalist  Army 
Invested  with  the  Executive  Power 

This  is  a  revolutionary  book.  To  whom  should  I  dedicate  it 
better  than  to  the  leader  of  the  greatest  and  most  transcen- 
dental revolution  that  ever  occurred  in  Mexico?  I  beg  you 
to  accept  it,  not  only  as  a  token  of  our  old  friendship,  but  as 
a  tribute  to  the  man  who  has  in  his  hands  the  reconstruction 
of  our  beloved  country.  THE  AUTHOR. 

City  of  Mexico,  January,  1916. 


CONTENTS 

INTRODUCTORY  REMARKS  . i 

Explanation  of  the  term  "  tendency." 
The  real  structure  of  the  musical  scale. 
Mathematical  ratios  between  scale-degrees. 
Greater  tone,  lesser  tone,  half-tone. 
The  syntonic  comma. 
Arrangement  of  the  major  scale. 
Tendencies  of  the  ;th,  4th  and  6th  degrees. 
The  Law  of  Lesser  Effort. 

—  The  2d  degree  also  obeys  this  law. 
Degrees  i,  3  and  5  do  not  obey  it. 

—  MUSICAL  CHORDS 4 

Definition  of  the  term  "chord." 
tj-~ 

The  Science  of  Harmony. 

<*•  HARMONIC  SYSTEM  BASED  ON  FOUR  FUNDAMENTAL  CHORDS.  .       5 
•       Tables  of  these  chords  and  their  derivatives. 

CHORD  I :    ORDINARILY  CALLED  THE  TONIC  CHORD 6 

o 
t  CHORD  OF  THE  V  —  DOMINANT  NINTH-CHORD 6 

**       Its  harmonic  tendency. 
^       Chords  V,  VII  and  II  derived  from  it. 

Their  harmonic  tendencies  and  regular  progression. 
These  chords,  and  the  Tonic  chord,  are  natural. 
Irregular  progression  of  natural  triads. 

Free  progression  of  the  Tonic  triad. 

o 
CHORD  OF  THE  II : 10 

A  mixed  chord;  its  law  of  movement  is  duplex. 
Mixed  chords  IV  and  VI  derived  from  it. 
These  chords  have  two  tendencies. 

Chords  IV  and  VI  preceded  by  chord  I. 

e 
Irregularly  preceded  by  natural  chords  derived  from  the  V. 

Chords  IV  and  VI  interconnected  regularly  and  irregularly. 


vi  CONTENTS 

8  PAGB 

THE  FUNDAMENTAL  MIXED  CHORD  VI 13 

Its  law  of  movement  is  duplex. 
•  Its  derivative,  the  mixed  chord  III,  has  two  tendencies. 

Mixed  chord  III  followed  by  natural  chords. 

Followed  by  the  mixed  chords  IV  and  VI. 

Preceded  by  natural  and  mixed  chords. 
FULL  FOUR-TONE  CHORDS,  OR  SEVENTH-CHORDS 15 

Tables  showing  derivation  from  the  four  great  chords. 
DOMINANT  SEVENTH-CHORD  V;    ITS  TENDENCY 16 

7 

SEVENTH-CHORD  ON  THE  yTH  DEGREE,  VII;    TENDENCY 17 

Regular  and  irregular  progression  of  natural  seventh-chords. 

7 

SEVENTH-CHORD  ON  THE  20  DEGREE,  II ;    DOUBLE  TENDENCY     18 
Preceded  by  natural  seventh-chords. 

7 

SEVENTH-CHORD  ON  THE  4TH  DEGREE,  IV;    DOUBLE  TENDENCY     20 

Regular  and  irregular  progression. 
SEVENTH-CHORD  ON  THE  6TH  DEGREE,  VI;    DOUBLE  TENDENCY     21 

Regular  and  irregular  progression. 

7 

SEVENTH-CHORD  ON  THE  IST  DEGREE,  I;    DOUBLE  TENDENCY     22 
Regular  and  irregular  progression. 

7 

SEVENTH-CHORD  ON  THE  30  DEGREE,  III;   DOUBLE  TENDENCY     24 

Regular  and  irregular  progression. 
CONNECTIONS  OF  SEVENTH-CHORDS  WITH  TRIADS 26 

7 

Natural  V  with  all  Natural  Triads;  with  Mixed  Tnads 27 

7 

Natural  VII  with  all  Natural  Triads;  with  Mixed  Triads.  ...      28 

7 

Mixed  II  with  Natural  Triads;  with  Mixed  Triads 29 

7 

Mixed  IV  with  Natural  Chords;  with  Mixed  Triads 30 

7 

Mixed  VI  with  Natural  Triads ;  with  Mixed  Triads 31 

7 

Mixed  I  with  Natural  Triads  ;  with  Mixed  Triads 32 

7 

Mixed  III  with  Natural  Triads;  with  Mixed  Triads 33 

TRIADS  FOLLOWED  BY  SEVENTH-CHORDS 34 

7 

By  the  Natural  Chord  V 34 

By  the  Natural  Chord  VII 35 

By  the  Mixed  Chord  II 36 

By  the  Mixed  Chord  IV 37 

By  the  Mixed  Chord  VI 38 


CONTENTS  vii 

7  PAGE 

By  the  Mixed  Chord  1 38 

By  the  Mixed  Chord  III 39 

MINOR  SCALE  AND  MINOR  KEYS 40 

CHROMATICS:    EFFECT  OF  CHROMATIC  ALTERATIONS 40 

ALTERED  OR  CHROMATIC  CHORDS 41 

MODULATION 43 

Forty-nine  Modulations  from  C  major  to  G  major 44 

Thirty-five  Modulations  from  C  major  to  D[?  major 51 

Six  HARMONIZATIONS  OF  A  CANTUS  FIRMUS,  BY  A  PUPIL.  ...  53 

CONCLUSION 55 


A  NEW  SYSTEM  OF  HARMONY 
BASED  ON  FOUR  FUNDAMENTAL  CHORDS 


A  well-known  fact  in  the  domain  of  science  is  the  great  im- 
portance of  a  good  classification.  The  classification  that  I  shall 
explain  here  is  based  on  four  fundamental  chords,  and  is  marked 
by  a  clearness  and  simplicity  not  ordinarily  found  in  books 
treating  on  this  subject. 

Every  well  instructed  musician  knows  that  the  classification 
now  employed  groups  the  musical  chords  according  to  their  form: 
and  so  we  have  major  chords,  minor  chords,  chords  of  the  sixth, 
of  the  sixth  and  fourth,  chords  of  the  seventh,  of  the  fifth  and 
sixth,  of  the  third  and  fourth,  of  the  second,  and  so  forth,  according 
to  certain  intervals  that  are  found  in  them. 

Since  Rameau  (eighteenth  century)  this  classification  has 
served,  it  is  true,  to  explain  and  teach  musical  Harmony;  but 
surely  very  many  have  felt,  as  I  always  have,  that  even  after 
learning  to  write  and  play  musical  chords,  it  always  remains  a 
kind  of  mystery  to  employ  them  in  a  musical  way,  and  this  is 
especially  true  of  the  triads  and  their  inversions. 

As  you  will  see  further  on,  in  my  classification  the  chords  are 
grouped  according  to  their  tendencies,  making  families  of  chords 
which  obey  the  same  law,  irrespective  of  their  form. 

The  books  on  Harmony  teach  that  chords  of  the  seventh  have 
certain  prescribed  movements  —  or  "resolutions,"  as  they  are 
called  —  but  they  also  teach  other  movements  or  resolutions 
considered  as  exceptional.  Talking  about  the  triads,  which 
are  treated  first,  they  say  that  these  are  more  difficult  to  handle, 
being  more  free  in  their  movements;  to  guide  you  they  estab- 
lish certain  fixed  and  almost  inflexible  rules  that  leave  you  in 


2  A   NEW  SYSTEM  OF  HARMONY 

the  dark  as  to  their  origin  and  reason.  What  is  worse,  there 
are  many  text-books  that  do  not  say  anything  about  the  move- 
ments of  these  chords. 

The  truth  about  this  —  and  I  consider  it  a  real  discovery  of 
mine  —  is  that  the  triads  also  have  a  tendency,  as  well  as  the 
dissonant  chords,  and  that  this  tendency  is  the  same  when  both  — 
triads  and  chords  of  the  seventh  —  have  the  same  fundamental 
and  come  from  the  same  origin  or  great  fundamental  chord. 

But  now  let  us  leave  criticism  of  the  known  systems,  and 
speak  about  the  new  classification  and  its  results.  I  hope  that 
my  fellow  musicians  will  find  it  clear,  easy  and  logical,  and, 
above  all,  practical  and  useful  for  the  teaching  of  musical  com- 
position. 

To  make  perfectly  plain  the  laws  that  govern  the  movements 
of  musical  chords,  it  is  necessary  to  go  back  to  the  musical  scale 
itself  on  which  modern  music  is  based.  If  we  consider  the  real 
musical  scale  and  not  the  conventional  one  ordinarily  explained 
in  musical  books,  we  find  the  following  facts: 

(1)  It  has  eight  sounds  or  degrees,  called  C,  D,  E,  F,  G,  A, 
B,  C  in  the  key  of  C. 

(2)  The  mathematical  ratios,  as  given  in  Acoustics,  between 
each  degree  and  the  fundamental,  or  first  one,  are  as  follows: 

1 

C  ,     D         E        F-G        A        B         C 

1      I      II      I      I      ¥      2 

Here  follows  the  explanation  of  this  figuring:  If  we  take  a  C 
of  240  vibrations,  the  D  —  or  second  degree  —  whose  ratio  is  f, 
will  have  9  vibrations  in  the  same  time  that  C  has  8,  or  (com- 
pleting the  computation),  240  X  9  -5-  8  =  270  vibrations  for  D; 
and  so  forth. 

Now,  if  we  want  to  know  the  mathematical  ratios  between  all 
the  contiguous  degrees  of  the  scale,  we  shall  find  them  by  dividing 
the  greater  one  by  the  lesser.  Taking  C  as  i,  we  aready  have 


ACOUSTICS:    LAW  OF  LESSER  EFFORT  3 

the  ratio  of  D  to  C,  or  f .  The  ratio  between  D  and  E  is  found  by 
dividing  f  by  f  =  f  £  =  -^-,  which  is  the  ratio  between  the 
second  and  third  degrees  of  the  scale;  and  so  forth. 

Below  are  given  the  ratios  between  all  contiguous  degrees  of 
the  scale: 

2 

CDEFGAB-C 

~T  IT  IF  T'  ™  ~T  TT 

On  inspection  we  can  see  at  once  three  different  relations  and, 
at  the  same  time,  three  different  kinds  of  intervals.  The  one 
represented  by  f  is  called  the  greater  tone;  the  one  represented 
by  ^j-  is  called  the  lesser  tone.  The  difference  between  a  greater 
tone  and  a  lesser  tone  is  found  by  dividing  their  respective  ratios 
as  follows:  f  -f-  *£-  =  f^.  This  difference,  amounting  to  f^-,  is 
called  in  Acoustics  a  syntonic  comma. 

As  not  everybody  is  inclined  to  mathematical  calculations,  I 
will  present  the  scale  and  its  intervals  in  the  following  table : 

3 
CDEFGABC 

greater    lesser       half-    greater    lesser    greater     half- 
tone      tone        tone      tone        tone       tone       tone 

Little  by  little,  as  music  was  changing  from  the  church  modes 
to  the  modern  scale,  musicians  felt,  empirically,  the  tendency 
of  certain  degrees  of  the  scale  to  proceed  to  some  other  degrees. 
These  tendencies  are  acknowledged  in  Harmony  text-books  as 
follows:  The  seventh  degree  tends  to  the  eighth,  the  fourth  degree 
tends  to  the  third,  and  the  sixth  degree  tends  to  the  fifth.  I  must 
state  that  many  books  do  not  even  mention  the  tendency  of 
the  sixth  degree. 

If  we  study  attentively  the  last  example  we  shall  notice 
that  the  seventh  degree  (B)  has  on  the  right  an  interval  of  a 
half-tone,  while  on  the  left  the  interval  is  a  greater  tone;  so  when 
B  shows  a  tendency  to  C,  it  tends  to  where  the  interval  is  smaller. 


4  A   NEW  SYSTEM  OF  HARMONY 

Looking  now  at  the  fourth  degree  (F),  we  notice  that  it  has  a 
greater  tone  on  the  right  and  a  half-tone  on  the  left;  so,  when  F 
shows  a  tendency  to  E,  it  is  again  where  there  is  a  smaller  interval. 
Considering  the  sixth  degree  (A),  we  see  that  on  the  right  is 
a  greater  tone,  while  to  the  left  is  a  lesser  tone;  so,  when  A  tends 
to  G,  it  tends  to  the  side  where  there  is  a  smaller  interval,  just 
as  in  the  other  two  cases  examined. 

These  three  particular  cases,  in  which  each  degree  tends  to 
the  side  where  the  interval  is  smaller,  authorize  us  to  deduce  a 
law  that  may  be  thus  expressed:  The  degrees  of  the  scale  which 
have  a  tendency,  obey  the  law  of  lesser  effort. 

Seeking  now  for  another  degree  of  the  scale  that  may  conform 
to  this  law,  we  find  the  second  degree  (D),  which  is  placed  between 
unequal  intervals,  having  on  the  right  a  lesser  tone  and  on  the 
left  a  greater  torn;  therefore,  the  second  degree  must  obey  the 
established  law  of  lesser  effort  and  have  a  tendency  to  the  third 
degree  (E).  As  there  is  no  book,  that  I  know  of,  assigning  any 
tendency  to  the  second  degree,  I  consider  that  the  tendency  now 
spoken  of  is  a  real  discovery  that  must  be  taken  account  of  in  a 
modern  method  of  musical  composition. 

The  law  of  lesser  effort  can  not  be  applied  to  the  first  (C),  third 
(E)  and  the  fifth  (G)  degrees  of  the  scale,  because  the  first  is 
the  fundamental  of  the  scale  and  G  and  E  are  strong  overtones 
of^C,  blending  with  it  so  closely  as  to  give  almost'the  same  sen- 
sation. 

MUSICAL   CHORDS 

The  simultaneous  sounding  of  three,  four  or  five  tones  at 
the  interval  of  a  third  from  one  another  is  called  a  musical  chord. 
The  study  of  chords  and  their  connections  is  known  as  the 
Science  of  Harmony. 

According  to  the  new  system  to  be  explained  here,  the  whole 
harmonic  structure  is  based  on  four  fundamental  chords  of  five 
tones  each.  These  five-tone  chords  are  called  in  Harmony 
chords  of  the  ninth;  their  root-tones  are  the  ist,  5th,  2d  and  6th 
degrees  of  the  scale,  respectively. 


THE  FOUR  FUNDAMENTAL   CHORDS 


5 


In  the  following  table  the  fundamental  chords  are  represented 
in  whole  notes.  The  first  chord  and  the  fourth  have  four  notes 
in  common  (C,  E,  G,  B),  as  shown  by  brackets.  The  chords 
in  quarter-notes  are  three-tone  chords  derived  from  the  great 
chords. 

HARMONIC   SYSTEM    BASED    ON    FOUR   FUNDAMENTAL 

CHORDS 


vvnii 


IV  VI 


This  form  may  be  better  represented  by  Arabic  figures  than 
by  notes.  And  I  say  better,  because  the  figures  stand  for  de- 
grees of  the  scale,  irrespective  of  the  tonality  or  key,  and  are 
applicable  to  all  the  keys;  whereas,  the  form  with  notes,  in  the 
foregoing  tables,  applies  only  to  the  key  of  C.  We  ought  to  have 
one  form  which  fits  every  key. 

4  bis 


Natural  Chords 

f 

Mixed 

Chords 

7 

7 

5 

/5\      5 

6 

6 

3 

i 

6 

3 

i    i 

©6     6 

3 

1 
6 

0  U  ' 

4 

4     4 

4 

4 

• 

/T\     m 

ej  (2) 

2 

222 

2 

(VI)     W 

1  i  (7) 

7 

7     7 

(II)          vi 

5 

5 

5            II 

IV 

3 

VII 

1 

V 

9 

9 

• 

I 

(V) 

V  VII  II 

IV  VI 

(VI) 

in 

6  A  NEW  SYSTEM  OF  HARMONY 

Playing  the  first  chord  C-E-G-B-D  on  a  piano  or  organ  — 
all  the  tones  simultaneously,  of  course  —  in  the  key  of  C,  we 
feel  that  the  chord  produced  is  dissonant  and  gives  the  sensation 
of  movement  or,  in  other  words,  that  it  has  a  tendency  to  move 
and  proceed  to  another  chord.  Taking  out  the  second  degree 
(D)  marked  with  the  figure  2,  we  get  a  chord  of  four  tones 
(C-E-G-B,  in  the  key  of  C),  which  also  gives  the  sensation  of 
movement. 

CHORD  I:  ORDINARILY  CALLED  THE  TONIC  CHORD 

Now,  leaving  out  the  seventh  degree  (B),  marked  in  the  table 
with  the  figure  7,  we  get  a  chord  of  three  tones  (C-E-G  in  the 
key  of  C)  : 


This  chord  is  called  perfect  or  consonant,  and  playing  it  we 
get  a  sensation  of  rest,  as  G  and  E  are  overtones  of  C,  and  the 
three  together  sound  very  well,  giving  a  quiet  and  peaceful 
sensation.  The  figuring  of  this  triad  formed  on  the  first  degree 
of  the  scale  is  with  a  Roman  number  I  underneath,  as  it  is  in 
the  above  example. 


NINTH-CHORD 

Considering  now  the  second  chord  of  my  system,  that  is,  the 

o 

chord  of  the  ninth  on  the  fifth  degree  (5-7-2-4-6),  figured  V,  we 
notice  that  it  has  one  degree  —  the  fifth  —  in  common  with 
the  chord  I,  or  tonic  chord,  and  that  the  remaining  degrees 
(7-2-4-6)  are  precisely  those  that,  according  to  the  law  of  lesser 
effort,  have  a  tendency.  It  is  interesting  to  observe  here  that 
the  tendency  of  the  active  degrees  of  the  scale  is  just  as  urgent 
when  they  are  alone  in  the  melody,  as  when  they  come  together 


THE  DOMINANT  NINTH-CHORD  7 

in  musical  chords,  as  you  will  see  later.  The  strong  union  of 
melody  and  harmony  is  really  noticeable,  and  it  has  been  a 
great  mistake  in  the  text-books  to  treat  them  separately,  thus 
dividing  their  study. 

Playing  now  on  the  piano  the  dominant  ninth  chord,  or  ninth- 

Q 

chord  on  the  fifth  degree  (which  is  perhaps  more  clear) ,  V,  we  feel 
at  once  a  very  strong  sensation  of  movement,  which  is  quite 
natural,  as  this  chord  has  in  it  the  four  degrees  of  the  scale 
(7,  2,  4,  6)  that  have  a  moving  tendency.  As  the  tendency  of  each 
of  these  degrees  is,  individually,  toward  a  degree  of  the  tonic 
chord  or  chord  I,  the  natural  tendency,  or,  as  we  may  say,  "the 

e 

law  of  movement"  of  the  chord  V,  is  to  go  to  chord  I: 


• 

II 

^^^^    — 

9   ^^^|» 

J 

^^^^  J 

Jj 

cv    \ 

M 

• 

J'     1 

N              '1 

! 

"**•—  •*' 

• 

'                    ' 

r 

o 

V       I. 

9 

3      v 

1 
i 

As  the  V  chord  has  five  sounds  and  chord  I  only  three,  it  has 
been  necessary,  in  this  example,  to  double  two  notes.  We  may 
also,  and  this  is  more  convenient,  divide  up  the  great  chord  into 

o 

three  chords  of  three  tones  each;   the  great  chord  V  now  becomes 

the  father  or  great  fundamental  of  three  smaller  chords  based, 
respectively,  on  the  5th,  yth,  and  2d  degrees  of  the  scale,  which 
give  them  their  names,  and  which  are  figured  with  Roman  nu- 
merals, as  follows: 

7 


,     II 

i 

\>\J          (^ 

• 

m     ! 

«J            ^                                      • 

_    -I  . 

• 

C\'       & 

**S 

V       VII        II 


8 


A   NEW  SYSTEM  OF  HARMONY 


Each  of  these  chords,  like  the  great  fundamental  chord  from 
which  they  come,  has  a  natural  tendency  to  the  tonic  chord  or 
chord  I;  and  this  is  easily  explained,  as  each  chord  (the  V,  the 
VII  and  the  II)  has  two  or  three  degrees  with  an  individual 
tendency  in  conformity  with  the  established  law  of  lesser  effort. 
So  the  following  connections  are  very  good: 


/r 

",•»—.«    i  53  sa    ii 

(o>  

• 

_ 

M  1 

—  J  i    1  J^    -1—  U 

«J 

^   ^ 

:     ^         Jl      /        _ 

Bm          m 

• 

i               i  i      i    F    1  1 

•  fc  ./r 

r         m 

1           >      II 

V        I,       V        I 


vii    i   VH     i,  vn    L 


n     i,    ii     i      ii      i 


\f 

I  call  the  first  two  chords  of  my  system  (the  I  and  the  V) 
natural  because  in  them  we  find  all  the  degrees  of  the  scale,  and 
one  or  the  other  may  harmonize  each  and  every  degree  in  the 
scale  itself  or  that  may  be  in  any  diatonic  melody. 

The  chords  V,  VII  and  II  are  also  natural,  because  they  are 

e 

found,  as  we  have  seen,  in  the  great  natural  V  chord,  and  com- 
bine between  themselves  easily,  preferably  in  a  contrary  direc- 
tion to  that  in  which  they  are  found;  they  were  derived  in  this 
order:  V,  VII,  II,  and  are  interconnected  in  the  reverse  order: 
II-VII-V,  or  II-V,  or  VII-V.  This  is  the  regular  and  logical 
progression  of  these  chords. 


11 


PROGRESSION  OF  NATURAL   TRIADS 


Regular  progression  of  natural  triads 


(fh  —  i  —  *  —  f- 

g*   h*  —  *— 

—  —  M  —  s— 

r=g  —  H 

s$     PI* 

E3      12 

«     •  i*     r 

E        H 

j    r-—  r 

n    vii     v 

™    f 
i         n      v 

r        t" 

I          VII        V 

I 

9*    «•  • 

—  ~-.  —  f-m  F— 

1  1  

II 

It  is  also  possible,  though  irregular,  to  combine  them  in  the 
same  order  that  we  found  them,  giving  them  a  sensation  of  going 
away  from  the  tonal  centre:  V-VII-II,  or  V-II,  or  VII-II. 

12 

Irregular  progression  of  natural  triads 

.    a  .  b   .          i  , 


yr       j 

|tf         5 

E          1  1 

irrv 

•         p 

sn 

^ 

r       II            A 

r 

v    v 

» 
ii   n 

r   r  ' 

I             V       II 

1 
I 

t-^  *       ^ 

It      m 

1  •        __ 

r      r 

2_ 

f 

The  tonic  chord  (I)  can  progress  freely  into  any  other  chord, 
as  it  has  not  any  degree  with  a  tendency;  so  the  following  con- 
nections are  very  good:  I-V,  I- VII,  I-II. 


13 


I  to  natural  chords  V-VII-II 


/L               •    1 

(?K     -        •         J 

• 

saz   z          i   8 

_ 

J  i    r 

V 

r 

VII 

i 

n 

c~\-                   ft 

i 

)• 

j 

c 

•S       4               t=E 

•   1 

• 

With  these  four  natural  triads  (I,  V,  VII  and  II)  we  have 
enough  elements  to  harmonize  any  melody,  and  there  are  nu- 
merous instances  in  which  the  great  masters  used  them  exclu- 
sively. From  Bach  to  Bellini  you  will  be  surprised  to  find  them 


IO 


A   NEW  SYSTEM  OF  HARAfONY 


harmonizing  beautiful  melodies;  also  see  the  first  part  of  "The 
Wedding  Chorus"  from  Wagner's  Lohengrin,  and  almost  any 
melody  of  Bellini,  the  world-famous  master  of  melody. 


CHORD    OF   THE    II 


Let  us  now  consider  the  third  chord  of  my  system,  that  is,  the 

o 

ninth-chord  on  the  superlonic  or  second  degree,  figured  II  and  com- 
posed of  degrees  2,  4,  6,  i,  3. 


14 


I 


o 

II 

This  is  a  mixed  chord,  as  it  has  three  degrees  (2,  4,  6)  from  the 

o 

natural  dominant  chord  V,  and  two  degrees  (i,  3)  from  the 
tonic  chord  I.     Its  law  of  movement  is  duplex,  for  it  may  go 

o 

naturally  towards  the  chord  V  as  well  as  towards  the  tonic 

chord  I,  because  it  has  notes  in  common  with  them  both: 

— — 

15  16 


V 

Dividing  up  the  chord  of  the  ninth  on  the  second  degree  (II) 
(2,  4,  6,  i,  3)  into  three  triads,  we  get 


2-4-6 

4-6-1 

6-1-3 

(ID 

TV 

VI 

17 

Mixed  triads 

r        & 

«      it 

~/4v  —  »  —  ' 

-f-»\- 

—  ^— 

—  1  H 

1C)    g  

'  ~ 

—  &^ 

—  •  H 

c/        ^ 
e 
II 

W 

IV 

VI 

PROGRESSION  OF  MIXED  CHORDS 


II 


One  of  these  chords  —  the  II  —  we  have  already  had;  but 
we  now  get  two  new  chords  —  the  IV  and  VI  —  that  are  based 
on  the  fourth  and  sixth  degrees  respectively. 

These  two  chords  (IV  and  VI),  like  the  great  chord  from 
which  they  come,  are  mixed  chords;  the  one  on  the  fourth 

9 

degree  (IV)  has  two  degrees  (4  and  6)  from  the  natural  chord  V, 
arui  one  degree  (the  I)  Ijrom  the  natural  chord  I.  The  chord  IV, 
or  subdominant  chord,  as  it  is  generally  called,  is  considered  in 
text-books  as  a  principal  chord  in  Harmony;  but  it  would  seem 
preferable  to  consider  it  a  mixed  chord. 

The  chord  VI  is  also  a  mixed  chord,  as  it  has  degree  6  from  the 

9 

natural  dominant  chord  V  and  degrees  i  and  3  from  the  natural 
tonic  chord  I. 
The  law  of  movement  of  these  two  mixed  chords  (IV  and  VI) 

0 

is  duplex;  they  may  pass  easily  to  the  derivatives  of  the  V: 


18 

Mixed  IV  in  regular  recessive  progression 
a    ,         i         ,  ,          I      b  i 


-/k  —  f  r~ 

-J  —  J  —  f  —  B 

*- 

-«  —  •— 

-J  —  ^  — 

-*&—?  *- 

~?  —  —  r5  —  r  '  r* 

~1  

-*  r  1 

J  r  r 

w    n, 

r   f  r   i    r 

n            na    iv 

n  tf  I         i         I         J 

vna 

i 

i   r 

i 

1   r 

vn 

V     J                         J 

1  1 

/L      i         m         f           i 

• 

j 

fPK    f     «I       »       J 

5 

S     II 

IV      V  Vx 

19 

Mixed  chord  VI  in  regular  recessive  progression 

*»      I         I    J-        I     J    b   I     J         I 


I*  \*\A 

m\\\  if -iff  if 


i 


^^ 


vi  na      nx       n   vi  vn     yna     vuz  vi  v 
or  directly  to  chord  I: 


12 


A   NEW  SYSTEM  OF  HARMONY 


20  21 

Mixed  IV  foil,  by  nat.  I :  Reg.  progression     Mixed  VI  foil,  by  nat.  I :  Reg.  prog. 

.    4 J        i        !      -J-       I 


• 


r 


The  mixed  chords  IV  and  VI  may,  very  well,  follow  the  chord  I 
(that  is,  I-IV  and  I- VI),  not  only  because  they  have  degrees  in 
common  with  that  chord,  but  also  because  the  tonic  chord  can 
go  to  any  other  chord,  as  it  has  not  any  degree  with  a  tendency. 


22 

Nat.  I  with  mixed  IV.     Reg. 


23 

Nat.  I  with  mixed  VI.     Reg. 


IV 


IV, 


IV 


r  i. 

r  ii 

Lastly  come  the  connections  of  the  mixed  chords  IV  and  VI 
preceded  by  natural  triads.  These  connections,  though  irregular, 
are  possible,  and  give  the  sensation  of  going  away  from  the  tonal 
centre: 


24 

Irregular     . 

J.        j 

25 

.     .     progression     ....     of 

J     J     J..  J     J     J 

.     .     .     .     natural     . 

—  ~j{~  —  9  1_  M~ 

—  i  —  2  —  j 

—  *— 

0  *  M 

ct)  1  —  »  —  t 

—  P  1  '-H-f  (•  F- 

—  p  \  —  U 

J    1      1 

V       IV 

26 

chords 

1       p 
iVj          iva   vn  iv, 

26  bis 

1  1  P  l_l 

T 

IVa              IV 

J1    J  ?  1 

.        J 

V 

:     J     1 

~^f 

!  -      m. 

II  •       _L  1  * 

•nma         —  i 

^n.           ,  -X"**. 

«          !        j 

112      f*  I-S 

«i 

-  |(j)    -m         -1           9 

_^  ^_ 

—  H-l  —  *-M  —  g  i  i  —  *  —  i 

r"T 

f  r  ' 

r 

IV 


IV         V       VI 


VI 


NINTH-CHORD   OF  THE  SUPERDOMINANT 


VII 


m 


f  -  r 


VI 


VI 


f 

VI 


VI 


The  mixed  chords  IV  and  VI  may  be  interconnected  in  any 
order,  as  their  fundamentals  are  separated  by  an  interval  of  a 
third  and  give  the  impression  of  being  a  single  chord  of  four 
tones:  IV- VI  is  good,  but  VI-IV  is  better  and  more  used  for 
its  regular  recessive  progression: 


27 


Reg.  progression  of  mixed  chords 
I     _J          I        J-          1? 


28 

Irreg.  progression  of  mixed  chords 


CHORD    OF   THE  VI,   ALSO    CALLED    NINTH-CHORD   OF 
THE   SUPERDOMINANT 

29  _ 


I 


w         e 
VI 

This  is  the  fourth  chord  of  my  system.     It  has  two  degrees 

o 
(the  6  and  7)  from  the  natural  dominant  chord  V,  and  three 

degrees  (1,3  and  5)  from  the  natural  tonic  chord  I.     This,  then, 
is  a  mixed  chord,  and  being  a  mixed  chord,  its  law  of  movement 

e 

is  duplex;  it  can  go  equally  well  either  to  V  or  to  I: 
30  31 


J    J      J    -1 


9  9 

VI  V 


9 
VI 


i 


A   NEW  SYSTEM  OF  HARMONY 


Dividing  up  the  chord  VI  (6,  i,  3,  5,  7)  into  three  triads  we 
have: 

6-1-3  1-3-5  3-5-7 

(VI)  (I)  (HI) 

32 

Mixed  chord  III 

(t)=t 


o 
VI 


III 


Here  are  two  chords  that  we  have  already  had  (VI  and  I), 

and  a  new  triad,  the  III.     This  triad  III  has  one  degree  —  the  7 

B 

—  from  the  natural  V,  and  two  degrees  —  the  i  and  3  —  from 
the  natural  chord  I.     Thus  it  is  a  mixed  chord,  like  the  great 

9 

chord  VI  from  which  it  conies,  and  its  law  of  movement  is  duplex; 

o 
it  can  pass  easily  to  the  derivatives  of   the   chord  V  (that  is, 

III-II,  III-VII,  III-V): 

33 

Mixed  III  with  nat.  1 1- VI  I- V  and  I :  Reg.  prog. 


tarn 


34 


i  35  J 

ti^l*)M  '   /T 


'  -  r 

m   vn 
or  directly  to  I  (III-I) : 


in     v 


m 


iid 


•* 


I 


in     i 


FULL  FOUR-TONE  CHORDS,   OR  SEVENTH-CHORDS  15 

The  connections  of  the  mixed  chord  III  with  the  other  mixed 
chords  VI  and  IV,  in  regular  regressive  order,  are  also  good  and 
much  recommended  in  the  usual  text-books: 


37  38 

Mixed  III  with  mixed  VI :  Reg.  progr.     Mixed  III  with  mixed  IV :  Reg.  progr. 


^m 


a 


T-T-T 


f 


III      VI 


VI 


In 


In  fact,  these  last  two  connections  are  the  only  ones  recom- 
mended by  some  writers,  but  the  great  composers  also  employ 
triad  III  with  the  connections  given  in  Examples  33,  34,  35  and 
36.  This  is  quite  logical,  as  triad  III  is  a  mixed  one,  and  has 

9 

notes  in  common  with  the  natural  chords  I  and  V.  Hence,  the 
relation  of  triad  III  to  both  chords,  as  well  as  to  their  deriva- 
tives, is  evident.  There  is,  therefore,  no  reason  to  limit  the 
connections  of  this  triad  with  IV  and  VI,  as  is  done  in  most 
text-books  on  Harmony.  The  mixed  triad  III  may  follow,  in 
irregular  order,  every  natural  three-tone  chord,  and  also  every 
other  mixed  chord: 


39     Mixed  III  preceded  by  nat.  triads. 


40     Mixed  III  preceded 
"by  other  mixed  triads. 


yr       i 

m      1  m 

m      i 

m     1 

•     II 

* 

• 

m 

f\\ 

1  r  - 

P 

*     1 

§       f 

9 

II 

\JJ      a 

' 

-"         1 

'"••^ 

1 

II 

i 

II 

I 

V 

V 

11 

] 

1    . 

I              ^ 

n 

i 

V 

r-\  • 

II 

1 

m                         II 

Iz 

T. 

r 

t 

*             f 

^r          i 

9 

FULL  FOUR-TONE  CHORDS,  OR  SEVENTH-CHORDS 

The  full  four-tone  chords,  or  "chords  of  the  seventh,"  as  they 
are  called,  are  also  found  in  the  four  great  chords  of  my  system, 
as  may  be  seen  here: 


16 


A  NEW  SYSTEM  OF  HARMONY 


41 


Chords  of  the  seventh  (four-tone  chords)  derived  from  the  four  fundamental  chords 


n 

Natural  chords                   11  Mixed  chords                                              1 

!         i     i    -«-     J    t 

v 

Iff 

J         fl     1     /5> 

tit 

/T 

_ 

& 

I         1 

• 

|(TV 

K> 

& 

I            *      1      /5 

i         II 

\,J 

& 

E 

i        9    I 

«_/' 

9        m         &           '0 

POO 

IV                                 II                                  VI 

<S                     «               • 

t^' 

Sr                      ^V 

•               1 

T. 

5?     1 

1 

2      1 

1      1 

7  7 

v    vn 


7  7 

II          IV 


7  7 

VI  I 


41  bis 

Natural  chords 

Mixed  chords 

1 

i 

7 

5 

5          5 

3 

3 

3 

3          3 

i 

i      i 

1 

1           1 

6 

6 

6 

6        6 

6 

6 

4 

4          4 

4 

4        4 

2 

2          2 

2 

2 

/  »  \ 

5 

7 
5 

7          7 
5 

(fi) 

(VI) 

3 

1 

9 

(V) 

7             7 

v     vn 

7          7 
II       IV 

7             7 

VI        I 

I 

I  will  treat  them  in  the  order  in  which  they  develop,  that  is, 
from  left  to  right,  this  being  their  logical  order  and  also  the 
order  of  their  importance  and  frequency  of  employment. 


.     SEVENTH-CHORD   ON   THE   DOMINANT   (FIFTH    DEGREE) 

FIGURED   V 

This  very  important  and  useful  chord  is  found  in  the  natural 

0 

chord  V,  and  is  also  a  natural  chord.     It  is  formed  by  degrees  5, 
7,  2  and  4,  the  last  three  of  which  have  a  marked  individual 


SEVENTH-CHORD   ON  THE  SEVENTH  DEGREE        17 

tendency  according  to  the  law  of  lesser  effort.     Its  law  of  pro- 
gression is  to  connect  with  the  tonic  triad  or  chord  I: 

42 


The  text-books  call  this  connection  "the  natural  resolution 
of  the  dominant  seventh-chord." 

SEVENTH-CHORD    ON    THE    SEVENTH    DEGREE, 
FIGURED   VII 

o 

This  chord  is  also  found  in  the  natural  chord  V;  hence,  it  is  a 
natural  chord.  It  is  formed  by  degrees  7,  2,  4  and  6,  all  of  them 
having  a  marked  tendency  according  to  the  law  of  lesser  effort. 
Its  law  of  movement  is  to  the  tonic  chord  or  triad  I: 

43   . 


I 


7 

VII 


I 


7  7 

To  connect  the  VII  with  the  V  in  regular  regressive  order  is 
very  easy  and  natural.  These  chords  developed  as  follows:  V 
and  VII;  they  return  to  the  tonal  centre  in  reverse  order, 

7         7 

VII-V: 

44 


/K       •        *  

m  —  i  —  *— 

7             7 

VII       V             I 

f\  • 

_,.*_..  —  «  — 

i8 


A   NEW  SYSTEM  OF  HARMONY 


We  notice  here  that  the  VII,  instead  of  obeying  its  law  of 

7 

progression  (going  directly  to  I),  passes  to  V,  "which  has  the  same 
tendency  to  the  tonic  triad;    this  effect  is  nothing  more  than  a 

7 

prolongation  of  the  same  tendency.     The  connection  of  the  VII 

7  77 

preceded  by  the  V,  that  is,  V-VII,  is  also  good,  though  irregular, 

7 

as  the  progression  of  the  V  is  not  toward  the  tonal  centre,  but 
away  from  it: 

45 

irreg. 


/L       3 

s?              1 

o    2 

a 

5*             II 

7 

7 

V 

VII            I 

BT— 

—  j  —  n 

-^       ,     1            J 

E           1 

(te 


SEVENTH-CHORD    ON    THE    SECOND    DEGREE,    FIGURED    II 

7  9 

The  chord  II  is  derived  from  II;  it  is  formed  by  degrees  2,  4, 

o 
6  and  i,  the  2, 4  and  6  being  from  the  natural  chord  V,  and  degree 

I  from  the  natural  chord  I.     Hence,  it  is  a  mixed  chord,  like  the 
great  chord  from  which  it  is  derived.     Its  law  of  progression 

9 

is  duplex,  for  it  tends  either  to  the  derivatives  of  V  (that  is, 

7  7 

VII  or  V): 


46 


47 


reg. 

-0  1  H 

i          - 

» 

it  *  J 

-&  —  H  — 

=rs*  H 

f(T\ 

H 

|l 

\^)         *           *  — 

—  /2?    " 

•          p 

«          '1 

J   r   i 

7             7 

n    vn 

q.    J     Jn 

1 

.  ] 
i 

i  "' 

7             7 
1           V 

J             J      | 

^r 

^  —  H  — 

—  ^     —  H 

»^                  *' 

i     n 

•J 

r   \  '/  i 

or  directly  to  I : 


SEVENTH-CHORD   ON  THE  FOURTH  DEGREE 


48 


reg. 


7 
II 


Going  away  from  the  tonal  centre,  the  mixed  chord  II  may  be 

7  777  77 

preceded  by  the  natural  chords  V  or  VII  (V-II  or  VII-II). 
Though  irregular,  this  progression  is  sometimes  employed,  but 
rectified  by  an  immediate  return  to  a  natural  chord  in  the  regu- 
lar way: 

49  50 

irreg.  irreg. 


fl            t 

S-  ' 

J 

J                         1            J            J 

J 

^        1  1        m-"^^ 

S          ll 

4 

J 

5^—  *  i 

B         II 

n  1  1                      i 

n                     fl—  —  ' 

in              II 

WJ      m 

»*         II        •                        • 

^              II 

«J 

7             1 

V        I 

! 

7 
[           V 

777 
VII         II            V 

i  1  n  1  1  

i  i  n 

^-\'i  —     •; 

—  j  —  H  —  —  •  

—  \  H 

—  1  

_j^^  — 

—  ^  H 

PUCCINI  :  "Tosca" 
51 

irreg.     irreg.  reg.  irreg.  reg.     irreg.  irreg. 


-\- 


^ 


=F=z 

77  7^777  7 

j^      v    vii      ii  vii    n    vii    n         iv 


i 


m 


i 


Key  E 


SEVENTH-CHORD   ON   THE   FOURTH    DEGREE,   FIGURED    IV 

This  chord,  usually  called  the  subdominant  seventh-chord, 

e 

is  derived  from  II.     It  is  formed  by  degrees  4,  6,  i,  3,  and  contains 

o 

two  degrees  (4  and  6)  from  the  natural  chord  V  and  two  degrees 


20 


A  NEW  SYSTEM  OF  HARMONY 


(i  and  3)  from  the  natural  chord  I.     It  is,  therefore,  a  mixed 

e 

chord,  like  the  II  from  which  it  comes,  and  its  law  of  progression 

e 
is  duplex,  as  it  tends  either  to  the  natural  chords  derived  from  V 

(that  is,  VII  or  V) : 


52 


reg 


reg. 


•0-     I 

| 

1 

T^t  JT~ 

—  z*—  |  

1  ^—  — 

—  =  H 

€t»-*  **— 

6  1 

V 

—  3  n 

£K^«  —  * 

I 

7             7 

IV     VII 

r    t 

I 

>^^,I  

7            7 
V         V 

r 

f~^\  •          ^-1 

1        i 

g 

-33 

JJ 

z 

or  directly  to  I: 


53 


4 


»r  r^rn 


This 


IV  may,  very  well,  be  followed,  in  regular 


regressive  order,  by  the  other  mixed  chord  II: 

54 

reg. 


/K     % 

-r. 

»rh= 

—  A  — 

^T~T    'f  f- 

7             7 

iv    n 

P— 

—  H  — 

2^-F-  

H  — 

-^  — 

or  preceded  by  it  in  irregular  progression: 


SEVENTH-CHORD   ON  THE  SIXTH  DEGREE 


21 


55 


irreg 


55  bis 

SCHUMANN:  Romanza 
Ich  grolle  nicht,"  meas.  7 


You  will  notice  that  these  two  chords  constitute  the  great 

8 

fundamental  chord  II  from  which  they  are  derived. 


SEVENTH-CHORD   ON    THE   SIXTH    DEGREE,   FIGURED   VI 

0 

Like  the  great  fundamental  chord  VI  from  which  it  is  derived, 

7 

the  chord  VI  is  a  mixed  one,  because  it  has  degree  6  from  the 

9 

natural  dominant  ninth-chord  V,  and  degrees  i,  3  and  5  from  the 
natural  tonic  chord  I.     Its  law  of  movement  is  therefore  dual  or 

9  77 

duplex;  it  may  go  either  to  the  derivatives  of  V  (that  is,  V  or  VII) : 

56     Mixed  VI 


3C    *  - 

ET 

• 

|(TV      ^' 

^— 

safe  2 

^*^ 

~*—*m 

J  C 

VI 

7              7 
V           VI 

i 

7 
VII 

pv-       * 

1      1 

T. 

I 

1 

or  directly  to  I: 


57 


reg. 


22 


A  NEW  SYSTEM  OF  HARMONY 


In  regular  regressive  order  to  the  tonal  centre  the  chord  VI, 
which  we  are  now  considering,  passes  very  easily  through  the 

e  77 

mixed  chords  that  come  from  II  (that  is,  IV  and  II) : 


58                                             59 

reg. 

I 

t/ 

•           - 

.-.  II    j       j 

1 

J 

, 

j/T" 

I 

•        fl 

J    J 

^   II    n        ^ 

•  • 

^ 

| 

f 

•           J 

• 

xQ}^ 

=-^*-«: 

«     1    « 

i*  a 

^ 

BE 

2 

ii 

;    t 

*   1  l-^f        » 

1 

1    '          C 

i  j 

77                                                      777 
VI          IV                                                VI(IV)II 

•^"^ 

vi(iv)n<vn)v 

(-*!' 

•*" 

^2 

II    i" 

^j 

f  

iH-H-  — 



~^+- 

= 

77  77 

The  inverted  irregular  progression  IV-VI,  or  II-VI,  is  also 
possible.  It  gives,  of  course,  the  feeling  of  going  away  from  the 
tonal  centre. 


60 

SCHUMANN  :  "Ich  grolle  nicht," 
measure  6 


7  7 

IV     irreg.    VI 


SEVENTH-CHORD    ON    THE    FIRST    DEGREE,    FIGURED    I 

7 

The  chord  I,  like  the  great  chord  from  which  it  is  derived,  is 

a  mixed  chord,  as  it  has  degree  7  from  the  natural  dominant 

e 

chord  V  and  degrees  i,  3  and  5  from  the  natural  chord  I. 

7 

Like  the  last  three  mixed  chords  that  we  have  studied  (VI, 

77  7 

IV,  II),  the  law  of  movement  of  I  is  duplex;  it  may  go  either 

e 

to  the  derivatives  of  the  natural  chord  V: 


SEVENTH-CHORD    ON  THE  FIRST  DEGREE 
61 

7 

Mixed  I 


/k—  «  f 

J_^2  _*  J        Q  J 

ggg  —  E 

4_^  —  |_.  —  |  &  —  1| 

V 

\ 
1 

J          1 

7            7 
I           V 

^  1  h 

r 
^P...     •*•  ,, 

( 

^)T—         -d= 

__^  —  H  H 

J       m         • 

—  h  —  1                 II 

or  directly  tc 

)I: 

62 

T^          M 

VL        2  ^*^^  4? 

//HA—"    J                    — 

V^l^                                 II 

< 
/ 

7 

/ 

CV-                                    II 

I 

T.                           0 

\ 

^       4 

In  regular  regressive  order  the  chord  I  goes  easily  through 
the  chords  already  studied: 

63 

«      I  ree-  I  I        I  II  I 


fa^t  i— 

-5      »  — 

—  ^  —  H 

*^*  +— 

J  ^ 

—  1  »  — 

J  i                              r 

77                 77                 77 

I        VI           IV      II          VII      V             I 

• 

*    1  • 

1 

^J 

or  it  may  skip  one  or  more  of  them : 


64 


65 

SCHUMANN  :  "Ich  grolle  nicht." 


777 
I  (VI)  IV 


=t=F 


— ^- 


^^1^ 


777 
I          (VI)         IV 


-0- 


3] 


A   NEW  SYSTEM  OF  HARMONY 


66 


reg, 


Si 

5^,8 

^  II 

7777                    \ 
I  (VI  IV)  II                     \ 

pv- 

i     » 

i              1  1 

T- 

. 

« 

9                          m     "••• 

—  m         A 

& 

The  irregular  progression  preceded  by  VI  (that  is,  VI-I),  is 

e 

good,  because  both  of  them  make  up  the  great  parent  chord  VI; 
nevertheless,  this  connection  is  not  frequently  employed: 


67 

irreg. 


\J 

/( 

i  : 

I/TV 

S32: 

^f 

J 

7 

VI 

7 
I 

tzv- 

m 

k  J. 

SEVENTH-CHORD   ON   THE   THIRD    DEGREE,   FIGURED    III 

7 

At  first  glance  the  chord  III  —  very  seldom  used  —  is  not 
found  in  my  system  of  four  fundamental  chords;  nevertheless, 
turn  back  to  the  first  chord  (i,  3,  5,  7,  2),  in  which  we  canceled 
two  degrees  (the  2  and  the  7)  to  make  it  consonant,  and  replacing 

7 

them,  we  find  chord  III  formed  by  degrees  3,  5,  7  and  2. 

68 

Mixed  chord  i 


I 


7 
III 


This  chord  is  also  a  mixed  one,  as  it  has  degrees  7  and  2  from 

o 
the  natural  dominant  chord  V,  and  degrees  i  and  3  from  the 

natural  tonic  chord  I.     Hence,  its  law  of  movement  is  duplex, 

O  t  7 

like  the  other  mixed  chords;  it  may  go  to  V,  or  its  derivatives  V 
and  VII: 


SEVENTH-CHORD   ON  THE   THIRD  DEGREE 


69 


70 


reg. 


reg. 


=4 


i 


7  7 

III          V 


7  7 

III       VU 


5 


or  directly  to  I: 


71 


reg. 


i 


7  \ 
III  \    I 


H 


In  regressive  regular  order  it  may  be  followed  by  all  the  mixed 
chords  already  studied: 


72 
a 


^=i=nrrn=j=H=:n 


77 
III  I 


77  77  77 

III       VI  III         IV  III        II 


§E^E|EE^EEI=|^=r=fl 


Though  irregular,  the  following  connection  is  good,  as  both 

6 

chords  make  up  the  great  chord  I  from  which  they  come: 


26  A  NEW  SYSTEM  OF  HARMONY 

CONNECTIONS    OF    SEVENTH-CHORDS    (FULL   FOUR-TONE 
CHORDS)    WITH    TRIADS    (THREE-TONE   CHORDS) 

In  these  connections  we  are  obliged  to  duplicate  one  degree  in 
the  triads,  so  that  we  may  have  four  notes,  but  they  continue  to 
be  considered  as  chords  of  three  real  tones. 

The  text-books  on  Harmony  teach  that  in  connecting  seventh- 
chords  with  triads,  the  seventh  of  the  first  chord  —  which  is 
dissonant  —  must  descend  one  degree  to  a  consonant  note  of 
the  triad;  they  call  this  "the  natural  resolution  of  the  seventh." 
But  here  they  make  a  mistake,  an  error  of  generalization.  Seeing 

7 

that  V  goes  naturally  to  I,  the  bass  going  up  a  fourth  and  the 
seventh  F  going  down  a  second,  they  generalized  from  a  single 
case  and  declared  that  all  dissonant  four-tone  chords  must  resolve 
in  a  similar  way,  the  bass  going  up  a  fourth  and  the  seventh 
going  down  a  second.  This  so-called  "rule  of  natural  resolu- 

7 

tion"  is,  however,  not  valid  when  we  come  to  the  chord  VII; 
for  now  the  bass  does  not  tend  to  go  up  a  fourth,  but  actually 
tends  to  go  up  only  a  second. 
My  classification  of  chords  and  their  laws  of  movement  is 

7  7 

much  more  logical,  as  the  natural  chords  V  and  VII  move  to 

7 

the  natural  chord  I,  or  tonal  centre,  while  the  mixed  chords  II. 

7  777 

IV,  VI,  I,  III  have  a  dual  law  of  movement,  going  either  to 

e 
the  derivatives  of  the  "natural  dominant  chord"  V,  or  directly 

to  the  "natural  tonic  chord"  I,  as  you  may  choose.  The  con- 
necting of  the  "mixed"  chords  with  "other  mixed"  chords  of 
the  same  class  is  regular  when  their  progression  is  recessive; 
and  irregular,  when  their  connection  is  made  in  the  other  direc- 
tion. 

Here  follow  the  connections  of  all  the  seventh-chords  (four- 
tone  chords)  followed  by  triads  (three- tone  chords). 


PROGRESSIONS  OF  THE  NATURAL  CHORD  V 


NATURAL  CHORD  V  CONNECTED  WITH  ALL 
NATURAL  TRIADS 


74     Natural  V     followed  by  nat.  triads 
a .          i        b     .          •    '     c  _\        J        d 


& 


rr^ 


^ 


% 


VII 


II 


1 


t-f=^feEEEH 


(a)  V-L   Regular  progression;    seventh  goes  down  a  second. 

7 

(b)  V-V.     No  progression;  seventh  goes  up  a  second. 

7 

(c)  V-VII.     Irregular    progression;     seventh    goes    down    a 
second. 

7 

(d)  V-II.     Irregular  progression;  seventh  is  held  in  the  same 
part. 

CONNECTED  WITH  MIXED  TRIADS 

75  7 

Natural  V  followed  by  mixed  triads  B.  GODARD  :  Op.  66,  No.  2 

.    a  b  i      c  i       '  i  d 


WT^f  §3=S  SB  ***T 

i-J-'j 

a  

r    f    '    '                 ^ 

iv           vi           ni          v 

U.  * 

v  in 

ii 

'_d.         —  »-• 

i-          • 

fgffi 

i                  i 

}•   j           i 

—  1—\  hAP    I 

^  1  X 

2    _,  1 

'  —  1  —  ' 

-R-lMnh- 

—  *_  1 

"i 

^                   PUCCINI  :  "  Boheme  " 

nJJ-  tt..      ••••      i 

~P~" 

( 

< 

Pi—  "n 

1  1 

«     ^ 

Nil 

•MI              •                      J     m 

1 

\             ty 

m          II 

i             v  m 

I 

n 

*    J'ffUTtJI              P      -1           X                      1          *" 

111 

-^  ^0  tt     J     n     x         J       ' 

28 


A   NEW  SYSTEM  OF  HARMONY 


(a)  V-IV.     Irregular  progression;  seventh  is  held  in  the  same 
part. 

(b)  V-VL     Irregular  progression;  seventh  goes  down  a  second. 

7 

(c,  d,  e)  V-III.     Irregular   progression;    seventh  goes  up  a 
second. 

NATURAL   CHORD   VII    CONNECTED   WITH   ALL 
NATURAL  TRIADS 


7fi 
' 


Nat.  VII  with  natural  triads 


^i'H'r'1?55^ 

j-     -*      -ft-     3t^  9        » 


+ 

'9 

I  V 


vn 


n 


r    j    .g   *    r     r 

— *H 


fa)  VII-I.     Natural  progression;  seventh  goes  down  a  second. 

7 

(6)  VII-V.     Natural  progression;  seventh  goes  down  a  second. 

7 

(c)  VII-VTL     No  progression;  seventh  goes  up  a  second. 

7 

(J)  VII-IL     Irregular  progression;  seventh  keeps  in  the  same 


part. 


SAME   CHORD    CONNECTED   WITH    MIXED    TRIADS 

77 

With  mixed  triads 
-  a  i      b  c 


IV 


VI 


TF 
I 

III 


• 

(a)  VII-IV.     Irregular   progression;    seventh   keeps  in   the 
same  part. 

7 

(6)  VII- VI.     Irregular   progression;    seventh   keeps   in   the 
same  part. 


PROGRESSIONS  OF   THE  MIXED   CHORD  II 


29 


(c)  VII-III.     Irregular   progression;     seventh   goes   down   a 
second. 

MIXED    CHORD    II    CONNECTED   WITH    NATURAL   TRIADS 

78  7 

Mixed  II  with  natural  triads 

.   a  |  b  c  \      d  ,         i 

— « *r- , — 


PF=? 


±tr-nT"8=H 


r 

VII 


II 


\TT\r 


I 

(a)  II-L     Regular  progression;    seventh  keeps  in  the  same 
part. 

7 

(b)  II-V.     Regular  progression;  seventh  goes  down  a  second. 

7 

(c)  II- VII.     Regular  progression;  seventh  goes  down  a  second. 

7 

(J)  II-II.     No  progression;  seventh  goes  up  a  second. 


SAME    CHORD    CONNECTED    WITH    MIXED    TRIADS 

79 

With  mixed  triads 
a  b  c 


JB^a 


i 


IV 


VI 


in 


m 


i 


I 

(a)  II-IV.     Irregular  progression;   seventh  changes  part  and 
disappears  as  a  dissonance. 

7 

(6)  II- VI.     Irregular  progression;   seventh  keeps  in  the  same 
part. 

7 

(c)  II-III.     Irregular  progression;  seventh  goes  down  a  second. 


•0  A   NEW  SYSTEM  OF  HARMONY 

MIXED   CHORD    IV   CONNECTED   WITH    NATURAL  CHORDS 

80  7 

Mixed  IV  with  natural  chords 

a  bed 


fm         m     \ 

$d    1     fl 

i« 

3       II 

m 

* 

• 

• 

VMJ      -^               £               |«        1 

1     m  —  • 

0— 

r        tl 

I 

?sr:  *  *  —  i 

^          *T 

v            •" 

7H 

U 

Ri—  *  P- 

~~*  —  p  i  r 

,    I    • 

—  H 

z±z:      i  „    , 

*         . 

•       II 

(a)  IV-I.    Regular  progression;    seventh  keeps  in  the  same 
part. 

7 

(b)  IV-V.     Regular  progression;  seventh  goes  down  a  second. 

7 

(c)  IV-VTL     Regular  progression;  seventh  goes  up  a  second. 

(d)  IV-II.    Regular  progression;   seventh  goes  up  a  second. 


CONNECTED   WITH   MIXED   TRIADS 

81 

with  mixed  chords 

-  a   I     _\_      b   I  \       *  4  I 


— r 


(a)  IV-IV.    Stationary;  seventh  goes  up  a  second. 

7 

(b)  IV-VI.     Irregular  progression;  seventh  keeps  in  the  same 
part. 

7 

(c)  IV-m.    Irregular  progression;  seventh  keeps  in  the  same 
part. 


PROGRESSIONS  OF  THE  MIXED  CHORD  VI 


MIXED  CHORD  VI  CONNECTED  WITH  NATURAL  TRIADS 


82     Mixed  IV 
followed  by  natural  triads 


r!    t  I  !^  I  !_  J  I  L  ?    H 
if   r  if   r  if^*?  if— ^   " 

• 


vn 


n 


(a)  VI-I.     Regular  progression;    seventh  keeps  in  the  same 
part. 

7 

(b)  VI-V.     Regular  progression;  seventh  goes  up  a  third. 

7 

(c)  VI- VII.     Regular    progression;     seventh    goes    down    a 
second. 

7 

(d)  VI-II.     Regular  progression;  seventh  goes  down  a  second. 


CONNECTED   WITH    MIXED    TRIADS 

83     Mixed  IV 
foil,  by  mixed  triads 


IV 


VI 


in 


I 


I 

(a)  VI-IV.     Regular  progression;   seventh  goes  up  a  second. 

7 

(b)  VI- VI.     Stationary;  seventh  goes  up  a  second. 

7 

(c)  VI-III.     Irregular  progression;  seventh  keeps  in  the  same 
part. 


A   NEW  SYSTEM  OF  HARMONY 


MIXED    CHORD    I    CONNECTED   WITH    NATURAL   TRIADS 


84     Mixed  I 

foil,  by  nat.  triads 
,    a  b   i          i      c    i          I      d 


tfr\— 

f  —  f-H| 

i  hf~"g  hf  —  i 

-H 

Ss2 

•      Si 

•  i  •     •  i  •     i 

n 

«_r 

- 

i 

s>-               -*- 

1           l     i 

v           vu            n 

—  m  —  i  —  1  1  1  1  1  — 

1T~i  1 

1  1  

—  *-J  —4— 

1                      1     #         • 

(a)  I-I.     No  progression;  seventh  goes  up  a  second. 

7 

(b)  I-V.     Regular  progression;    seventh  keeps  in  the  same 
part. 

(c)  I- VII.     Regular  progression;   seventh  keeps  in  the  same 
part. 

7 

(d)  I-II.     Regular  progression;   seventh  goes  down  a  second. 


CONNECTED   WITH    MIXED   TRIADS 


85 

foil,  by  mixed  triads 
a  b  c 


IV 


i  U  J  H 


VI 

i-J. 


in 


i 


• 

(a)  I-IV.     Regular  progression;  seventh  goes  down  a  second. 

7 

(b)  I-VI.     Regular  progression;  seventh  goes  up  a  second. 

7 

(c)  I-III.     Irregular  progression;  seventh  goes  down  a  third. 


PROGRESSIONS  OF  THE  MIXED  CHORD  III  33 


MIXED    CHORD    III    CONNECTED   WITH    NATURAL   TRIADS 

86     Mixed   III 
foil,  by  natural  triads 
a  b  c  d 


EH—  1        01 

I         •     1 

5        -IS 

*ll 

^K                   •      ' 

p        to    |    • 

II 

33  ' 

'  C 

*               ^P 

1 

VII 

P 
II 

cv   •  \  1  1 

1    1 

1     I 

•         II 

j'  P  \i 

• 

•                    P 

—  f  —  H 

2?                  # 

« 

r         J 

(a)  III-I.     Regular  progression;   seventh  goes  up  a  second. 

7 

(6)  III-V.     Regular  progression;   seventh  keeps  in  the  same 
part  but  vanishes  as  a  dissonance. 

7 

(c)  III-VIL     Regular    progression;     seventh   changes   part 
and  vanishes  as  a  dissonance. 

7 

(d)  III-II.     Regular  progression;   seventh  keeps  in  the  same 
part. 


CONNECTED   WITH    MIXED   TRIADS 

87 

foil,  by  mixed  triads 

a  b  c 


L, ,    /  |        ,     M 

F      ^^f      -F- 


f 


IV  VI 


III 


S 


H^_ 


I 


(a)  III-IV.     Regular  progression;  seventh  goes  down  a  second. 

7 

(6)  III-VI.     Regular    progression;     seventh    goes    down    a 
second. 

7 

(c)  Ill-Ill.     No  progression;  seventh  goes  up  a  second. 


34  A   NEW  SYSTEM   OF  HARMONY 

TRIADS    FOLLOWED    BY    SEVENTH-CHORDS 


We  have  seen  seventh-chords  connected  with  triads.  We  are 
now  going  to  see  triads  connected  with  chords  of  the  seventh. 

Besides  the  laws  of  movement  that  we  are  familiar  with,  we 
must  keep  in  mind  another  important  condition.  The  practice 
of  the  great  masters  was,  from  the  beginning,  to  prepare  the 
dissonance  in  the  chords  of  the  seventh,  that  is,  to  make  the  same 
sound  appear  as  a  consonance  in  the  preceding  chord.  Mon- 
teverde,  a  great  Italian  composer  (1567-1643),  was  the  first  to 
let  the  seventh  enter  free,  that  is,  not  prepared,  in  the  dominant 

7 

seventh-chord  (V),  and  from  that  time  this  usage  has  been 
respected;  nevertheless,  all  the  remaining  seventh-chords  were 
kept  under  the  primitive  rule  and  had  to  prepare  the  seventh. 

7  7 

In  my  system,  the  chords  V  and  VII,  being  natural  chords, 
may  have  the  seventh  free;  but  the  remaining  four- tone  mixed 

77777 

chords  II,  IV,  VI,  I,  III,  must  enter  with  the  seventh  prepared. 
A  modern  practice  is  to  consider  as  sufficient  preparation  coming 
down  a  degree  when  both  chords  have  the  same  fundamental, 
as  you  will  see  in  the  examples  below. 

All  these  precautions  are  to  be  strictly  observed  in  vocal 
part-music,  but  in  instrumental  or  free  style  music,  modern 
composers  take  many  liberties  in  the  handling  of  the  seventh- 
chords.  The  attentive  reading  of  works  by  good  masters,  and 
a  musically  educated  ear,  are  a  sure  guide  to  the  young  composer. 

THE   NATURAL   CHORD  V 

May  follow  any  natural  or  mixed  triad;  e.g.  : 

88     Nat.  V 
nat.  triads 


TRIADS  FOLLOIVED  BY  SEVENTH-CHORDS 


35 


(a)  I-V.     Seventh  free. 

(b)  V-V.     Seventh  free. 

7 

(c)  VII-V.     Seventh  prepared. 

7 

(d)  II-V.     Seventh  of  the  second  chord  heard  in  another 
part  of  the  first  chord. 

89 

mixed  triads 

.  Vl       J_    6 


» w 


IV 


VI 


III 


(a)  IV-V. 
(6)  VI-V. 


Seventh  prepared. 
Seventh  free. 


(c)  III-V.     Seventh  free. 


i 


NATURAL   CHORD   VII 


May  follow  any  triad. 


90    Nat.  VII 
natural  triads 
a    \          \       b                      c                      d 

n      n                             '                                                                '                                           ' 

1  y 

1!                    1 

IA                 1  1 

/L       • 

_i              * 

II 

fm     * 

«J          » 

Q 

\^V     m 

<             1         |      4 

p>                 i| 

| 

f                            ' 

V                   VI 

*           ^        * 

i             n 

1    1*               1 

•     i           in 

1               •            • 

. 

K 

1            •         • 

*      J 

(a)  I-VII.     Seventh  free. 

(b)  V-VII.    Seventh  free. 

(c)  VII-VII.     Seventh  free. 

7 

(d)  II-VII.     Seventh  prepared. 


A  NEW  SYSTEM  OF  HARMONY 


91 

mixed 
a 

triads 
b 

e 

\j         <*•  ">- 

| 

III 

S(           r 

m                  , 

fn\    f 

*         1 

if 

^K      f          ' 

» 

f             n 

Er     r-  - 
IV                   VI 

-J-        J           *        J 

-?- 
in     i 

r"V  •            A 

r 

I»     M 

« 

*       * 

1          • 

r            II 

(a)  IV-VII.  Seventh  prepared. 

7 

(b)  VI-VII.  Seventh  prepared. 

(c)  III-VII.  Seventh  free. 


MIXED   CHORD   II 

Cannot  follow  V,  VII,  or  III  because  the  seventh  cannot  be 
prepared. 


92     Mixed  II 
natural  triads 


a  ^_ 

^  1     *                *                <f  1 

1  1  1  1  2— 

I     .. 

—f-                                                                           \-±~ 

^¥— 

|{T\       « 

01                                  1                                   1      * 

*     n 

r       1                           1                           IB 

r    •• 

V 
I 

P 

v   ^          vn   &         ii 

r 

C^\  * 

*i                 i                 i 

•    M 

1» 

I                 I                 I   • 

* 

^J           9 

1                 1                 1   * 

ii 

(a)  I-II.     Seventh  prepared,  good. 

7 

(6)  V-II.     Bad,  because  seventh  is  not  prepared. 

7 

(c)  VII-II.     Bad,  because  seventh  is  not  prepared. 

7 

(d)  II-II.     Seventh  enters  by  a  second  down;    rjermitted, 
because  both  chords  have  the  same  fundamental. 


IV 


VI 


in 


i 


PROGRESSIONS  TO  THE  MIXED  CHORD  IV 


37 


(a)  IV-II.  Seventh  prepared,  good. 

(b)  VI-II.  Seventh  prepared,  good. 

7 

(c)  III-II.  Bad,  because  seventh  cannot  be  prepared. 


MIXED    CHORD    IV 


Cannot  follow  VI,  VII,  or  II  because  the  seventh  cannot  be 
prepared. 


94    Mixed  IV 
natural  triads 

a  \_  ^  |       b 

C                            d 

JL   ? 

—r-[-          —  1— 

~H 

*&—»     *- 

1  1  

H 

i 

-9- 

V     ft) 

VII     ft)           II     (t) 

C\' 

m       | 

II 

T. 

•       1 

1 

1 

(a)  I-IV.     Good;  seventh  prepared. 

(b)  V-IV.     Bad. 

(c)  VII-IV.     Bad. 

(d)  II-IV.    Bad. 


95 

mixed  triads 
a  I 

-* 


r 


IV 


VI 


in 


^-M  1 1  r  r 


1 


(a)  I  V-IV.     Seventh  prepared  by  a  second  down;  permitted, 
because  both  chords  have  the  same  fundamental. 

(b)  VI-IV.     Good. 

(c)  III-IV.     Good. 


A   NEW  SYSTEM  OF  HARMONY 


MIXED    CHORD   VI 


More  used  than  IV  and  less  used  than  II :  cannot  follow  VII, 
II  and  IV  because  the  seventh  cannot  be  prepared. 


96     Mixed  VI 
natural  triads 

v    a   I  I  b 


vii 


n 


(a)  I-VI.     Good. 
(6)  V-VI.     Good. 
(c}  VII-VI.    Bad. 
(<I)  II-vY    Bad. 


97 

mixed  triads 
a  b 


*       Is          |          /J 

iWfL 


* 


IV 


VI 


in 


(a)  IV-VI.    Bad. 

7 

(b)  VL-VI.     Seventh  prepared  by  a  second  down;   permitted, 
because  both  chords  have  the  same  fundamental. 

(c)  III-VI.     Good. 


MIXED    CHORD    I 


Cannot  follow  II,  IV  and  VI  because  the  seventh  cannot  be 
prepared. 


PROGRESSIONS  TO   THE  MIXED   CHORD  III 


39 


7 

98     Mixed  I 
natural  triads 

r\a               1^1                   c  \ 

J     * 

~m  1  —               —  T| 

UT\  —  •         *  — 

f    i  h-p^ 

^_J  __T 

v^L/ 

i  • 

w     i                  1  1 

i    T    y   "T    vii 

ii   $• 

^:  J    ? 

=p=k*- 

5  —  "  —  i  — 

3  1  

(a)  I-I.     Good. 

(b)  V-I.     Good. 

(c)  VII-I.     Good. 

(d)  II-I.     Bad. 


99 

mixed  triads 
n    a                      £ 

c 

\       t 

m,  "^  i 

'     M 

m       \ 

. 

ifh               I 

f        ! 

I     II 

SI2                            1 

~     ii 

IV     •$•             VI     •$• 

1         1 
HI 

py.                                      | 

1  1 

a»                    1 

m 

j     II 

^                     I 

r      i 

' 

1 

II 

(a)  IV-I.     Bad. 

(b)  VI-I.     Bad. 

(c)  III-I.     Good. 


MIXED    CHORD    III 


This  is  the  least  used  of  all  the  chords  of  the  seventh.  Can- 
not follow  triads  I,  IV  and  VI,  because  the  seventh  cannot  be 
prepared. 

100     Mixed  III 


/L 

I    m         m       I    m 

•    i 

II 

(G>  

1—  *  *       1     p 

—  »    \—% 

-f  — 

-^                           'y^                         VII 

\ 
ii 

f 

r~v- 

1m                               1 

*-J. 

r      m       m 

« 

^S 

r  .      *.. 

r 

40 


A   NEW  SYSTEM  OF  HARMONY 


(a)  I-III.     Bad. 

(b)  V-III.     Good. 

(c)  VII-III.     Good. 

(d)  II-III.     Good. 


101 

a         b 

! 

| 

/                          1                         1 

"1'--^ 

H 

/                          1 

3'     •»• 

M 

c\                      1                      1 

l 

ll 

V  )                                 1                                 1 

ii 

IV    ty            VI    &             I 

II 

C\*                                            |                                            | 

T*                           I                          1 

P  ^^^^ 

^                             1                           1 

(a)  TV-Ill.    Bad. 

(b)  VL-lll.    Bad. 

7 

(c)  Ill-Ill.     Seventh  prepared  by  a  second  down;  permitted, 
because  both  chords  have  the  same  fundamental. 


MINOR   SCALE   AND    MINOR   KEYS 

The  laws  that  have  been  established  for  major  keys  are  appli- 
cable in  every  case  to  the  minor  keys. 


CHROMATICS 

Chromatic  alterations  to  single  degrees  of  the  scale  produce 
the  following  results: 

(i)  When  applied  to  a  tranquil  scale-degree  (i,  2,  or  5),  chro- 
matic alteration  gives  it  a  tendency  to  go  in  the  same  direction  that 
the  alteration  points;  that  is,  if  the  alteration  is  a  sharp  (or  a 
natural,  in  the  flat  keys),  the  tendency  imparted  is  to  continue 
upward: 


ALTERED   OR   CHROMATIC  CHORDS 


102 


«T 


When  the  alteration  is  aflat  (or  a  natural,  in  the  sharp  keys), 
it  gives  tranquil  degrees  a  tendency  to  go  down: 


103 

3 


I 


(2)  In  case  the  chromatic  alteration  is  applied  to  an  active 
scale-degree  (7,  4,  5,  or  2),  it  will  intensify  the  tendency  of  the 
said  degree  if  it  is  in  the  same  direction  as  the  tendency: 
104 


pN^d=fl 


-*=-#* 

Or  it  will  change  the  said  tendency  when  the  alteration  is  in  a 
contrary  direction. 


105 

4 


ALTERED    OR   CHROMATIC   CHORDS 

All  that  has  been  said  here  of  chromatic  alterations,  when 
applied  melodically  to  single  notes,  is  also  good  when  we  come 
to  altered  chords. 

The  natural  chord  I,  that  has  no  particular  tendency,  acquires 
one  when  it  becomes  an  altered  chord: 

106  107  108 

ii  i 


i 


r 


e 


I 


i 


Ij 


7 

VII 


• 


42  A   NEW  SYSTEM  OF  HARMONY 

7  7 

The  natural  chords  V,  VII,  II,  V  and  VII,  which  have  a  ten- 
dency to  proceed  to  the  natural  tonic  chord  I,  intensify  this 
tendency  when  they  become  altered  chords: 


109 

I 

110                      111 

112 

£/     0 

"fe  ^  —  It*  —  ffi  F  —  II        ir  F  —  H 

9        a9          2         II 

•\    m 

~~?  —  ~^»  —  •  —  H 

ft                         l_lZjK            V 

• 

[ 

js                     a      Je                     a      fa 

r       r 

M 

•        _ 

i*               11^                 !      1  1  ^                 Ill 

i*      •             M 

•       ™ 

r         _i    ii 

•                             •        1                    * 

I                m 

III                          III                          II 

'                       M 

V       I           IIj  VII3    I          II      H!     I 

113                             114                           115 

1              1      J        J             J 

7          7 

v     v3 

yl    7. 

J      II    m      ru        •      II 

1  1 

In?  ^ 

—&  •  H-?  VZ  H—  f  fc  •  H 

InzS 

-&*—         —  f  H-jr—          —  f  H—  i— 

•p  —  s  —  » 

r  i    r     r 
LJ         J   5  J- 

r  r 

I  I^-V1 

B. 

H 

VBl 

—  p  —  ^ 

'  1(— 

y 

77                                                 7                                                 7 

va    v3     i         v   vn     i               vna 

« 
The  chromatic  alterations  employed  in  the  mixed  chords  IV, 

7                    7 

II  and  IV  make  them  lose  the  faculty  that  they  had,  at  the 
o 

choice  of  the  composer,  to  go  to  the  derivatives  of  the  V,  and 
give  them  a  decided  tendency  to  the  tonic  chord  I: 

116                            117                         118 

J>  d  .      3  ii  3  fe=  3  »i  J^J  -j-n 

|p 

'     v*  —  *—  H  .     II  £—'i 

T  r  r 

ba        a             a        - 

b      a          $     bf      *          5     ft1 

^-f-H 

e 
•t 

i^ 

»  —  ^  —  H 

—  P  1  H—  '  '  1  H  5 
IV      IV      Ij           IV     JIV!     I                       1 

7 
i!        Ia 

119 


MODULA  TION 

120  121 


43 


I 


ir 


I 


9 


A 

J 


I 


I 


7  7 

II          II 


I 


On  the  contrary,  the  chromatic   alterations   in   the   mixed 

7 

chords  VI,  VI  and  I,  make  them  lose  the  ability  to  go  to  the 
tonic  chord,  and  give  them  a  decided  tendency  to  the  derivatives 
of  the  dominant  ninth-chord: 


122 


123 


124 


125 


t      bi 


I 


77 
VI        V 


777 
I      }VIa      Va          V 


MODULATION 

In  musical  Harmony,  modulation  means  a  change  of  key  or 
tonality;  by  extension,  the  change  of  mode  is  also  considered  as 
a  modulation.  Therefore,  we  may  say  that  MODULATION  is  a 
change  of  key,  or  of  mode,  or  of  key  and  mode  at  the  same  time. 
The  change  of  key  brings  a  change  in  the  function  of  the  tones 
(or  notes)  in  the  scale  and,  therefore,  a  change  in  the  function  of 
chords,  as  a  natural  Ionic  chord  may  become  a  natural  domi- 
nant, or  a  mixed  chord,  and  so  forth. 

The  principle  that  rules  modulation  is  very  simple  and  may  be 
stated  thus:  A  key  may  be  abandoned  at  ANY  CHORD  (natural, 
mixed  or  altered),  entering  the  new  key  through  ANY  CHORD  (nat- 


44 


A   NEW  SYSTEM  OF  HARMONY 


ural,  mixed  or  altered).  The  last  chord  of  the  old  key  escapes, 
of  course,  the  laws  previously  established;  but  the  first  chord 
of  the  new  key  is  governed  by  the  said  laws,  and  must  obey 
them. 

The  author  believes  that  the  place  to  treat  thoroughly  of 
modulation  is  in  a  method  of  Harmony  based  on  his  system; 
nevertheless,  it  may  not  be  out  of  place  here  to  give  a  sample 
of  the  almost  unlimited  resources  that  the  principle  just  stated 
about  modulation  puts  in  the  hands  of  the  composer.  There 
are  more  than  two  thousand  ways  of  leaving  a  key.  It  is  not  im- 
possible that  some  of  the  extravagances  of  the  ultra-modern 
composers  in  striving  after  novelty  is  due,  in  good  part,  to  the 
many  restrictions  of  the  accepted  books  on  Harmony. 

Here  follow,  as  a  sample,  forty-nine  different  ways  of  effecting 
a  modulation  from  C  major  to  G  major,  employing  only  chords 
of  three  tones.  If  we  choose  to  use  four-tone  chords  (chords  of 
the  seventh),  we  shall  have  another  forty-nine  different  ways  of 
effecting  the  same  modulation.  There  will  be  some  fifteen  or 
twenty  more  new  ways  if  we  employ  altered  chords!  What  a 
wealth  of  resources  for  a  single  modulation  like  this! 

Leaving  the  Key  of  C  major  at  I  and  entering  G  major,  suc- 
cessively, through  I,  V,  VII,  II,  W,  VI,  III. 
1  234 

J*M 


*FF 


3P^ 


r 


T 


r 


mRF^a 


1 


VII 


n 


VI 


in 


MODULATION 


45 


Leaving  the  Key  of  C  major  at  V  and  entering  G  major, 
successively,  through  I,  V,  VII,  II,  IV,  VI,  III. 


i 


*p 


V     G  I 


V     G  V 


10 


11 


1 

1 

r«^L 

i                  i 

J    &- 

^ 

yX  "* 

0  

~*/5  

—                          —4— 

'  —  %  —  1 

~^~ 

1?T\      A 

•^                n 

~                  f 

\ 

\>L/         • 

II       ^ 

\\ 

1 

„       1T_£_      p 

r~ 

-f   ^^ 

^"T  1  

_j^  

1  —  ^  —  H  —  i  1  — 

-  r      '  — 

~?  H 

3£ 

1 

1                  ! 

i          II 

V    GVII 


V       Gil 


12 


V  GIV 


13 


tfo   ^    " 

—, 

T~sr= 

—  iS>  —                  •  — 

-*—tir 

3  — 

VvJ      £ 

f 

•                               A 

p   0 

.  p  u 

t^-r      r-r 

-•-        •        T?- 

i  "i    i      r   f    i  i!i 
•ft- 

1 

Oil         !           M 

i     u 

^J-  —  *  i  

HE 

_  p  —  ^  — 

E3  —  H 

V  G  VI 


14 


r 


V  GUI 


46 


A   NEW  SYSTEAf  OF  HARMONY 


Leaving  the  Key  of  C  major  at  VII  and  entering  G  major, 
successively,  through  I,  V,  VII,  II,  IV,  VI,  III. 


15 


16 


i 


II 


-• — p 


i  r  f 


•* — •- 


§T 


^§P 


C       VII  G  I 


c    VUG v 


17 


18 


*=£ 


T=3E 


i 


-•     p 


r    P  '  0 

I      I       I 


1K 


C        VII  G  VII 


c     vn  GH 


19 


20 


.    A                  i 

!     ^ 

ol 

£ 

|          | 

-#  9  1— 

-J  —  i 

T? 

||       J 

I 

^T^     ~~ 

•  — 

-• 

K  

jg         II       * 

• 

—  - 

-0  m.  — 

"       • 

t 
' 

A 

j  r  i 
i 

1 

r 

r 

^ 
i 

T 

a* 

T-               J 

f 

—  m 

*-.  . 

4 

c     VTIG  iv 


C      VTIGVI 


21 


XL       • 

a 

__* 

2 

ft\ 

3 

^^ 

H 

3  H 

TO     - 

Bi 

ftr 

J  r 

T 

-P-     « 

"T" 

1" 

c\-             i 

r 

J 

S           ii 

as    I        ' 

r          II 

c      vn  G  m 


MODULATION 


47 


Leaving  the  Key  of  C  major  at  II  and  entering  the  Key  of 
G  major  through  I,  V,  VII,  II,  IV,  VI,  III. 


22 


23 


xL      I       t 

—  J- 

f  —  • 

i  —  • 

il  *  —  : 

-*  —  H 

BEE2  —  ±- 

-^  — 

*-d 

-£* 

^E  —  r 

-J 

—  tiS  — 

-f  H 

«j         • 
J-   J 

r  ' 

I   "! 
i 

r  • 
-•- 

P 
1 

"T" 

.     * 

r 

c\.             z 

Hfl 

<. 

j 

1         F 

f*1 

!       J 

.,   •_. 

C         II  G  I 


C        II  G  V 


24 


25 


XL                     •       * 

C 

&     \\             2 

• 

g        II 

ft>    m      •       * 

f 

i      M    •      i* 

r 

1 

II     » 

II 

«J      |                i 

1 

a*               •     \>zm        P 

£*     11             m 

tt 

/9              II 

T'                      i  <^ 

II     -i 

fl 

Z       * 

II    i 

II 

2( 

r~9  —  a 

\ 

\  

i-  ! 

1  ' 

2 

!7 

| 

J   j 

Jt- 

tff 

t  r 

3tZ 

BSE 

—  0  — 

-j  ^~ 

i=t 

irH    • 

1 

t 

ut 

I* 

f 

• 

Saz    r 

fl 

0 

r 

J    1 

^1 
-j  —  : 

f 

r 

1        ' 

•  —  i 

1      1 

i  i_  i 

aj 

—  * 

t  

f       J 

~~r1"h~ 

-f— 

i* 

•    ^ 

~H  —  H 

z     • 

• 

1     9 

•      c 

xJ 

C         II  G  IV 


C         II  GVI 


28 


X         i 

—           II 

fits 

1 

ig 

f? 

SB     « 

>l 

H 

d 

i              "1 

J  r 

i 

1 

1 

i 

£~\  • 

M* 

Z.       1 

] 

II  GUI 


48 


A   NEW  SYSTEM  OF  HARMONY 


Leaving  the  Key  of  C  at  IV  and  entering  the  Key  of  G 
through  I,  V,  VII,  II,  IV,  VI,  III. 


29 


30 


1 


II; 


C       IV  G  I 


C        IV  GV 


31 


32 


i* 

5c 


1 


C         IV  GVII 


C          IV  Gil 


33 


34 


1 


*t 


C          IV  GIV 


C          IV  G  VI 


35 


fo  •    »  p 

j  —  «- 

-i-^- 

^= 

gz=|  —  i  —  I  '>  —  *—\ 

p\*   i    •  -*  \  P 

—  <a  H 

j^—*— 

g 

H 

C         IV  G  III 


MODULATION 


49 


Leaving  the  Key  of  C  at  VI  and  entering  the  Key  of  G 
through  I,  V,  VII,  II,  IV,  VI,  III. 
36  37 


i 


=a* 


— r 


i 


i 


C       VI  G  I 


C       VI  GV 


38 


39 


^9- 


C        VI  G  VII 


C         VI  G  II 


40 


41 


1 


9t 


i 


^0 


C         VI  G  IV 


C          VI  G  VI 


42 


ri-  =n 


9t 


c       vi  GUI 


A   .\'EU'  SYSTEAf  OF  HARMONY 


Leaving  the  Key  of  C  at  III  and  entering  the  Key  of  G 
through  I,  V,  VII,  II,  IV,  VI,  III. 
43  44 


^ 


p      f 

I      I 


C         III  G  I 
45 


C         III    GV 

46 

I 


S 


I; 


*=:§£ 


C         III  G  VII 


47 


I          J 


C         III   Gil 
48 


m—    —  *— 

^            i 

! 

^9— 

j— 

w      • 

-^  H 

y^r  i 

i      r 

- 

f\'    ' 

1 

— 

— 

*         TV 

H-<a  M 

^-  —  ^  — 

B            < 

r~ 

;i 

i  —  i 

H 

III  GIV 


C          III  G  VI 


49 


xT      i 

fl 

ftv 

2 

u              1 

^K     i 

• 

X*               > 

*7     ,• 
1 

1 

T    i 

Ck* 

1 

f3              II 

y. 

I 

f 

' 

2:      < 

m           * 

II 

c        in  GUI 

The  composer  has  the  same  liberty  in  the  so-called  "extra- 
neous modulations."  Let  us  take,  as  an  example,  a  modulation 
a  minor  second  upward;  some  books  teach  one  way  only  of  effect- 
ing this  modulation,  namely,  "to  leave  the  old  key  at  the  tonic 
chord  (I)  and  to  enter  the  new  key  through  its  dominant  seventh- 

7 

chord  (V)."    Here  follow  thirty-five  different  ways  of  effecting 


MODULATION  51 

the  said  modulation,  leaving  the  old  key  at  the  tonic  chord. 
Imagine  how  many  more  ways  there  are  if  we  apply  the 
principle  of  "leaving  the  key  at  any  chord!" 

THIRTY-FIVE  MODULATIONS  FROM  C  MAJOR  TO  Db  MAJOR 

(that  is,  a  minor  second  upward),  starting  with  the  tonic  triad 

123  4 


VII, 


II 


J_  J   ,  J_fe*:       I        jJfc*:    ^J I 


16 


A   NEW  SYSTEM  OF  HARMONY 
17  18 


ff&- 


^ 


rff^rh^B 


19  20 

btW 


21 


jj  tJt^g 

•  uii   TT         iu— 


^=n"~T~l  L'.u!    ETt-ti   Ib>    1 1     .a    |bw n 

f^-gb  ^r^^^U-^M 


LJ?-L 


^       + 


vnij 


22 


23 


24 


i 


ivb 


25 


26 


27 


!.bJ 


J   b<  I,  W 
-I  h  ;ftri 

^  "!KZ  '     V 


^~- 


f 


iT     r^T 

»-M> 


^J-JJ^-H^W-L 


1 


Hi? 


ivb 


MODULATION' 


53 


32 


•     Pf    ,  ^r~Sg~H     *    \S 


33 


„  J   J  tj 

^^ 

jj  r    P-M- 


SI 


:n 


^ 


jtit 


7 


34 


In  order  to  show  the  rapid  progress  which  is  possible  when 
applying  my  system  of  Harmony  and  the  laws  and  principles 
derived  from  it,  I  append  a  melody  (given  subject)  harmonized 
in  six  different  ways  by  a  pupil  of  mine  after  he  had  taken 
thirteen  lessons!  I  must  say,  to  be  exact,  that  this  exercise  re- 
quired three  or  four  corrections. 


54 


A   NEW  SYSTEM  OF  HARMONY 


Given  Subject 


! 

s 

m 

:•           V        w 

0    w    m 

52       II 

1  (.([)      ^  ' 

!, 

.      t 

2 

m       *       m 

M 

t 

1 

•     f    p 

^   1 

\  r  r  " 

*        i« 

1  '-^*li  ff/i 

0      ' 

p 

-f  •  »•  h— 

—  —  H 

\  ~^~^^r^r]  — 

* 

p 

~ 

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CONCLUSION 


55 


m 


This  concludes  the  exposition  of  my  system.  I  call  it  a  new 
one  because  I  do  not  know  of  any  author  who  has  explained 
the  whole  system  of  harmony  based  on  these  four  fundamental 
chords.  It  is  not  a  mere  trifle,  or  an  object  of  mere  curiosity, 
for  the  laws  that  rule  melody  as  well  as  chords  have  been  deduced 
by  a  rigorously  scientific  method,  as  you  have  seen.  Further- 
more, these  rules  are  very  few,  eminently  practical,  and  easy  of 
application. 

I  have  read  many  times,  and  I  was  inclined  to  believe  so  my- 
self, that  the  true  method  of  musical  composition  ought  to  be 
deduced  from  the  practice  of  the  great  masters.  I  confess  here 
that  after  much  thinking  on  the  subject  there  came  to  my  mind, 
as  a  revelation,  the  group  of  four  fundamental  chords  that  make 
up  my  system;  the  laws  that  I  have  explained  here  are  the 
result  of  long  study  and  a  strict  application  of  scientific  prin- 
ciples. 

Having  discovered  the  laws,  the  next  step  was  to  see  if  the 
great  composers  had  observed  them  in  their  handling  of  musical 
material;  and  I  was  soon  convinced  that  they  had,  guided 
surely  by  the  fine  sense  and  marvelous  intuition  peculiar  to 
great  artists.  I  could  quote  innumerable  examples  that  prove 
what  I  have  said  here,  but  the  proper  place  for  these  will  be  in  a 
Method  of  musical  composition  still  to  be  written,  based  on 
this  new  classification  of  chords. 


56  A   NEW  SYSTEM  OF  HARMONY 

In  handling  the  musical  chords  under  the  laws  stated  here, 
you  are  conscious  of  what  you  are  doing;  this  (if  I  may  speak 
from  my  own  experience)  is  not  the  case  when  you  are  studying 
the  ordinary  text-books  on  the  subject. 

For  many  years  I  have  devoted  myself  to  the  study  of 
Pedagogy,  trying  assiduously  to  apply  its  principles  in  all  branches 
of  music-teaching.  Viewing  my  system*  from  the  pedagogical 
standpoint,  a  new  path  is  in  sight,  which  reveals  the  most  im- 
portant facts  for  writing  a  true  pedagogical  method  of  compo- 
sition —  a  method  in  which  melody,  harmony  and  counterpoint 
will  go  simultaneously  hand  in  hand,  as  the  real  friends  that 
they  are,  and  not  disconnected  one  from  the  other  as  it  has  been 
the  custom  to  present  them  heretofore. 

I  hope  that  the  foregoing  exposition  will  be  considered  by 
the  musical  world  with  the  attention  that  I  think  it  deserves; 
and  I  shall  be  glad  to  read  and  take  account  of  all  the  criticisms 
that  my  fellow  musicians  may  have  to  make  about  this  important 
subject. 

EDUARDO  GARIEL 

Tacubaya,  D.  F.,  suburb  of  the  City  of  Mexico 
October,  1915 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

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RECEIVED 

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UNIVERSITY'  OF  CALIFORNIA 

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